N2011 P1 Q3

The parametric equation of a curve are

\(x={{t}^{2}}\), \(y=\frac{2}{t}\)

1. Find the equation of the tangent to the curve at the point \(\left( {{p}^{2}},\frac{2}{p} \right)\), simplifying your answer.[2]
2. Hence find the coordinates of the points \(Q\) and \(R\) where this tangent meets the \(x\)- and \(y\)- axes respectively.[2]

3. Find a cartesian equation of the locus of (of the curve traced by) the mid-point of \(QR\) as \(p\) varies.

   [3]